COVID-19: A Surgical Perspective for when the curve flattens.

At the present time it is clear that our global healthcare community was not prepared to face the COVID-19 pandemic. Hospitals in the hardest hit areas have been transformed to COVID centres. Surgical societies have recommended postponing non-emergency surgery, and have given recommendations for triaging the ever- growing backlog of patients. However, simply resuming these non-emergency surgeries may lead the healthcare system into a second disaster. If healthcare policymakers around the world do not systematically consider how to resume normal surgical services, hospitals will be quickly overwhelmed, vital resources will be depleted, and patients and providers alike will face an increased exposure risk. This perspective serves to highlight certain aspects of returning to normal that physicians and hospital administrators alike must consider to avoid potential catastrophe

Direct Calculation of the Spin Stiffness in the J1J_1--J2J_2 Heisenberg Antiferromagnet

We calculate the spin stiffness $\rho_s$ for the frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a square lattice by exact diagonalizations on finite clusters of up to $36$ sites followed by extrapolations to the thermodynamic limit. For the non-frustrated case, we find that $\rho_s = (0.183\pm 0.003)J_1$, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for $0.4 \lesssim J_2/J_1 \lesssim 0.6$. In this intermediate region, the finite-size scaling works poorly -- an additional sign that their is neither N\'eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N\'eel-ordered region.Comment: 4 pages, uuencoded compressed ps-file (made with uufiles

Modified Spin Wave Thoery of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest and next-nearest neighbour intralayer interaction is studied by means of the modified spin wave method. For weak interlayer coupling, the ground state is found to be always magnetically ordered while the quantum disordered phase appear for large enough interlayer coupling. The properties of the disordered phase vary according to the strength of the frustration. In the regime of weak frustration, the disordered ground state is an almost uncorrelated assembly of interlayer dimers, while in the strongly frustrated regime the quantum spin liquid phase which has considerable N\'eel type short range order appears. The behavior of the sublattice magnetization and spin-spin correlation length in each phase is discussed.Comment: 15 pages, revtex, figures upon reques

Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach

We analyze the thermodynamic properties of the spin-S two-dimensional quantum Heisenberg antiferromagnet on a square lattice with nearest and next-nearest neighbor couplings in the Neel phase (J_2/J_1<0.4) employing the quantum hierarchical reference theory (QHRT), a non-perturbative implementation of the renormalization group method to quantum systems. We investigate the staggered susceptibility, the structure factors and the correlation length at finite temperature and for different values of the frustration ratio. From the finite temperature results, we also extrapolate ground state properties, such as spin stiffness and spontaneous staggered magnetization, providing an estimate of the extent of quantum corrections. The behavior of these quantities as a function of frustration may provide some hint on the breakdown of the Neel phase at zero temperature for larger values of J_2

Topological quantum memory

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.Comment: 39 pages, 21 figures, REVTe

Schwinger-boson approach to quantum spin systems: Gaussian fluctuactions in the "natural" gauge

We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated J1-J2 antiferromagnet on the square lattice shows that, unlike the saddle-point predictions, there is a quantum nonmagnetic phase for 0.53 < J2/J1 < 0.64. This result is obtained by considering the corrections to the spin stiffness on large lattices and extrapolating to the thermodynamic limit, which avoids the infinite-lattice infrared divergencies associated to Bose condensation. The very good agreement of our results with exact numerical values on finite clusters lends support to the calculational scheme employed.Comment: 4 pages, Latex, 3 figures included as eps files,minor correction

Quantum Phase Transition in the Frustrated Heisenberg Antiferromagnet

Using the J_1-J_2 model, we present a description of quantum phase transition from Neel ordered to the spin-liquid state based on the modified spin wave theory. The general expression for the gap in the spectrum in the spin-liquid phase is presented.Comment: 8 pages of REVTeX 3.0, one PostScript file appended (Eq. 15 corrected, two recent references added, + some minor changes

Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As the inter-chain coupling decreases we observe a transition in the anisotropic XY case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases are found to be qualitatively the same, however, in the regime of weak inter-chain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.Comment: to appear in Physical Review

Theory of anyon excitons: Relation to excitons of nu=1/3 and nu=2/3 incompressible liquids

Elementary excitations of incompressible quantum liquids (IQL's) are anyons, i.e., quasiparticles carrying fractional charges and obeying fractional statistics. To find out how the properties of these quasiparticles manifest themselves in the optical spectra, we have developed the anyon exciton model (AEM) and compared the results with the finite-size data for excitons of nu=1/3 and nu=2/3 IQL's. The model considers an exciton as a neutral composite consisting of three quasielectrons and a single hole. The AEM works well when the separation between electron and hole confinement planes, h, is larger than the magnetic length l. In the framework of the AEM an exciton possesses momentum k and two internal quantum numbers, one of which can be chosen as the angular momentum, L, of the k=0 state. Existence of the internal degrees of freedom results in the multiple branch energy spectrum, crater-like electron density shape and 120 degrees density correlations for k=0 excitons, and the splitting of the electron shell into bunches for non-zero k excitons. For h larger than 2l the bottom states obey the superselection rule L=3m (m are integers starting from 2), all of them are hard core states. For h nearly 2l there is one-to-one correspondence between the low-energy spectra found for the AEM and the many- electron exciton spectra of the nu=2/3 IQL, whereas some states are absent from the many-electron spectra of the nu=1/3 IQL. We argue that this striking difference in the spectra originates from the different populational statistics of the quasielectrons of charge conjugate IQL's and show that the proper account of the statistical requirements eliminates excessive states from the spectrum. Apparently, this phenomenon is the first manifestation of the exclusion statistics in the anyon bound states.Comment: 26 pages with 9 figures, typos correcte

Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model

The ground state parameters of the two-dimensional S=1/2 antiferromagnetic Heisenberg model are calculated using the Stochastic Series Expansion quantum Monte Carlo method for L*L lattices with L up to 16. The finite-size results for the energy E, the sublattice magnetization M, the long-wavelength susceptibility chi_perp(q=2*pi/L), and the spin stiffness rho_s, are extrapolated to the thermodynamic limit using fits to polynomials in 1/L, constrained by scaling forms previously obtained from renormalization group calculations for the nonlinear sigma model and chiral perturbation theory. The results are fully consistent with the predicted leading finite-size corrections and are of sufficient accuracy for extracting also subleading terms. The subleading energy correction (proportional to 1/L^4) agrees with chiral perturbation theory to within a statistical error of a few percent, thus providing the first numerical confirmation of the finite-size scaling forms to this order. The extrapolated ground state energy per spin, E=-0.669437(5), is the most accurate estimate reported to date. The most accurate Green's function Monte Carlo (GFMC) result is slightly higher than this value, most likely due to a small systematic error originating from ``population control'' bias in GFMC. The other extrapolated parameters are M=0.3070(3), rho_s = 0.175(2), chi_perp = 0.0625(9), and the spinwave velocity c=1.673(7). The statistical errors are comparable with those of the best previous estimates, obtained by fitting loop algorithm quantum Monte Carlo data to finite-temperature scaling forms. Both M and rho_s obtained from the finite-T data are, however, a few error bars higher than the present estimates. It is argued that the T=0 extrapolations performed here are less sensitive to effects of neglectedComment: 16 pages, RevTex, 9 PostScript figure